The Determination of Exchange Rates in International Asset ...PART VI The Determination of Exchange Rates in International Asset Markets Chapter 27 Expectations, Money, and the Determination

P A R T V I

The Determination of Exchange Rates in International

Asset Markets

Chapter 27 ■ Expectations, Money, and the Determination of the Exchange RatePAGE 573

Chapter 28 ■ Exchange Rate Forecasting and RiskPAGE 607

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573

CHAPTER 27

Expectations, Money, and the Determination of the Exchange Rate

We now turn our attention explicitly to the determination of exchange rates ininternational financial markets. In Chapter 23 we adopted the assumptionof perfect capital mobility, or perfect international integration of financial

markets: There are no transaction costs, capital controls, or other barriers separatinginternational investors from the portfolios they would like to hold. We will maintainthis assumption. Large quantities of capital are ready to move back and forth acrossnational boundaries at will. Because investors adjust their portfolios instantaneously inresponse to changes in rates of return, exchange rates are volatile. The exchange rate isnow the relative price of foreign versus domestic assets, rather than the relative price offoreign versus domestic goods. Thus it is not surprising that exchange rates turn out tobe as volatile as the prices of bonds, equities, gold, and other assets, in contrast to themuch more stable national price levels. Refer back to Figure 19.4 for an illustration ofthis volatility.

In Chapters 21 and 22, the international portfolio investor’s decision concerningwhat country’s asset to hold depended only on interest rates. This chapter introducesan additional factor that enters investors’ decision making: expectations about futurechanges in exchange rates. It was reasonable to omit this factor when we were studyinga fixed exchange rate and assuming the rate had little likelihood of being changed.Under the modern floating rate system, however, investors are forced to wager onexchange rate movements every time they invest internationally. We begin by focusingon a key building block of models of exchange rate determination: international inter-est rate parity conditions.

27.1 Interest Rate Parity Conditions

If the dollar is expected to lose value in the future against the yen, then Japaneseinvestors will subtract the expected rate of dollar depreciation from the dollar interestrate when contemplating the purchase of U.S. assets. Similarly, U.S. investors will addthe expected rate of yen appreciation to the yen interest rate when contemplating thepurchase of Japanese assets. If investors do not care about any factors other than the

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expected rates of return on the two countries’ assets, then they will buy the asset withthe higher expected return and sell the other, a process that continues until expectedreturns are equalized across countries. This means that the expected rate of deprecia-tion of the domestic currency, Dse, will be equal to the nominal interest differential.

i 2 i* 5 Dse (27.1)

This condition is known as uncovered interest parity.Uncovered interest parity is somewhat similar to covered interest parity, the arbi-

trage condition, Equation 21.2, introduced in Chapter 21:

i 2 i* 5 fd (27.2)

where fd is the forward discount. There is an important difference, however. In theabsence of transaction costs, capital controls, and so on, any deviations from Equa-tion 27.2 would mean that investors could risklessly make as much money as theywanted, simply by borrowing in the low-interest-rate country and lending in the other,covering on the forward exchange market. There would be no risk of capital losses (orgains) because the exchange risk is hedged on the forward exchange market. It is veryunlikely that such golden profit opportunities exist; indeed, Chapter 21 showed thatcovered interest parity holds for most industrialized countries.

Uncovered interest parity is another matter. Here investors buying a foreign assetwith an apparently high rate of return expose themselves to the risk that whatever isearned in interest will be outweighed by unexpected adverse movements in theexchange rate. Thus uncovered interest parity is a stronger hypothesis than coveredinterest parity. It will hold only if investors treat domestic currency and foreign cur-rency assets as perfect substitutes in their portfolios. In particular, uncovered interestparity will hold only if exchange risk is not important to investors. (This would be thecase if investors are relatively certain as to the future exchange rate or, alternatively,if they are risk neutral, i.e., they are unconcerned about risk.)

Expected depreciation and exchange risk are the two factors that can separatedomestic and foreign interest rates, even in the absence of barriers to internationalcapital movement. This chapter considers only expected depreciation. We considerexchange risk in Chapter 28.1

We will be using Equation 27.1 throughout this chapter. It is important to clarifyfrom the outset that the uncovered interest parity condition is not necessarily a state-ment about causality; it is not a model specifying the determination of interest rates.Equation 27.1 is an equilibrium condition. It is entirely consistent with the idea that theinterest rate is determined to give equilibrium in the money market, as assumed in pre-vious chapters. This chapter simply adds Equation 27.1 as one of the equations that willhave to be satisfied simultaneously if investors are to be happy with the portfolios theyare holding.

574 Chapter 27 ■ Expectations, Money, and the Determination of the Exchange Rate

1Note that if Equations 27.1 and 27.2 both hold, then we have fd 5 Dse. This is another way of saying there isno exchange risk premium in the foreign exchange market. (Equation 21.A.3 defined the exchange risk pre-mium. Chapter 28 will discuss it further.)

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27.2 The Monetary Model of Exchange Rates with Flexible Prices

Under the assumptions (1) that no transaction costs, government controls, or otherbarriers are discouraging international trade in bonds, and (2) that investors treat dif-ferent countries’ assets as perfect substitutes in their portfolios, it is as if there is onlyone type of bond in the world. Different countries’ bonds can be aggregated together,as long as they all pay the same expected rate of return; investors will be indifferent towhich country’s bonds they hold. This is what is meant by assuming uncovered inter-est parity.

The first half of the chapter will also make some analogous assumptions aboutgoods markets: (1) there are no transportation costs, government controls, or otherbarriers discouraging international trade in goods, and (2) consumers’ tastes are suchthat they treat different countries’ goods as perfect substitutes. Thus it is as if there isonly one type of good in the world. Countries’ goods can be aggregated together solong as their relative prices are fixed. This is what is meant by purchasing power parity,the condition covered extensively in Chapter 19. That chapter distinguished betweenthe monetary approach to the balance of payments, so named because it devotes spe-cial attention to international flows of money, and the monetarist and new classicalmodels, which add the assumption that prices are perfectly flexible so that goods mar-kets always clear. This chapter can be thought of as the monetary approach to theexchange rate, the floating rate version of the model studied in Chapter 19 for the caseof fixed rates. Only in the first half of this chapter do we add the assumption that goodsprices are perfectly flexible, to get what might be called the monetarist or new classicalmodel of the exchange rate.

Why return to the assumption of price flexibility, given all the evidence against itreported earlier? First, the model in which there is only one good as well as one bondin the world is a conveniently simple starting point from which to begin the explorationof the complexities of modern exchange rate theory. Second, purchasing power parity(PPP) is not a bad approximation for considering the very long run (or for consideringother cases where there are large changes in money supplies, price levels, and exchangerates, as in hyperinflation). Section 27.3 will reintroduce short-run deviations fromPPP: variation in the real exchange rate related to monetary disturbances in the pres-ence of sticky goods prices.

We first brought up the importance of exchange rate expectations at the end of thepresentation of the Mundell-Fleming model in Chapter 23, which assumed that priceswere fixed in the short run. The discussion there noted that investors might expect theexchange rate in the future to move, from wherever it happened to be at the moment,in the direction of long-run equilibrium. This is how we will model expectations in thischapter. First, however, it will be helpful to have an idea of the long-run equilibriumtoward which the exchange rate is expected to move. This is another reason for begin-ning here by studying the long-run equilibrium in which PPP holds.

We repeat the PPP assumption:

(27.3) S 5PP*

27.2 ■ The Monetary Model of Exchange Rates with Flexible Prices 575

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Here denotes the level of the exchange rate (the “spot” price of foreign exchange), Pthe domestic price level, and P* the foreign price level. Placing a bar over the exchangerate indicates that—ultimately—the equation is taken seriously only in long-run equi-librium. is on the left side here because the focus is on how exchange rates are deter-mined. This is in contrast to Chapter 19, which dealt with fixed exchange rates. Therethe domestic price level was determined by the exchange rate set by the government,so P was on the left side.

Equation 27.3 is incomplete as a theory of what determines the exchange ratebecause it simply pushes the question back one step. It says that the exchange ratemoves in proportion to the price level. What determines the price level?

The Exchange Rate as the Price of Money

The other essential equation in the monetary model of the exchange rate is the onethat sets the real supply of money, M P, equal to the real demand for money, L.

M P 5 L(i, Y) (27.4)

As in the derivation of the LM curve (Equation 22.4), this equation assumes that thedemand for money is a decreasing function of the interest rate, i, because people wishto hold less money when other assets pay a higher rate of return compared to money,but an increasing function of income, Y, because people have a greater need for moneywith which to undertake transactions when income is higher.2 To treat the relationshipas a theory of how the price level is determined, solve for P.

P 5 M L(i, Y) (27.5)

It makes sense to think of the price level as being determined to set money demandequal to money supply because prices are assumed perfectly flexible. Notice that a 10percent increase in the money supply causes the price level to increase by 10 percent.

The supply and demand for money in the foreign country is modeled in preciselythe same way.

P* 5 M* L*(i*, Y*) (27.6)

Now take the ratio of the two price level equations, and substitute it into Equation27.3.

5 5 (27.7)

Equation 27.7 has a simple intuitive interpretation.The exchange rate is defined asthe price of foreign currency in terms of domestic currency. Thus we are now modelingit as the relative price of foreign money rather than the relative price of foreign goods.As such, it should be determined by the relative supply and demand for money. Noticethat the foreign money supply, M*, appears in the denominator. An increase in M* will

M /M*L(i, Y) /L*(i*, Y*)

M /L (i, Y)M*/L*(i*, Y*)

S

/

/

/

/

S

S


2It is possible to derive a money demand function from principles of optimization. Robert Lucas, “InterestRates and Currency Prices in a Two-Country World,” Journal of Monetary Economics, 10 (1982): 335–360.

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5Equation 27.8 could be applied to a context of fixed exchange rates as easily as to floating rates, or to a con-text in which the central bank intervenes in the foreign exchange market to some intermediate degree. LanceGirton and Don Roper, “A Monetary Model of Exchange Market Pressure Applied to the Postwar CanadianExperience,” American Economic Review, 67, no. 4 (1977): 537–548.

4There is a particular functional form for L(i, Y) that allows the interest rates to enter in simple differenceform, as in Equation 27.8: the exponential function. The chapter supplement offers a formal presentation ofthe model in logs.

cause a decline in the price of foreign money—the exchange rate, —just as anincrease in the supply of bananas causes a fall in the price of bananas. An increase inthe demand for foreign money, L*, will have the opposite effect: an increase in theprice of foreign money, just as an increase in the demand for bananas causes anincrease in the price of bananas.What about the effect of domestic factors? The domes-tic money supply, M, is in the numerator. An increase in the domestic money supplycauses an increase in the exchange rate, a depreciation of the currency. (This is thesame result seen in previous chapters.) Finally, an increase in the domestic demand formoney causes a decrease in the exchange rate.

The nature of the exchange rate’s dependence on the money supplies is very sim-ple: It is directly proportionate to M and inversely proportionate to M*. When thedomestic money supply increases by 10 percent relative to the foreign money supply,the exchange rate goes up by 10 percent because the price level goes up by 10 percent.This is the property of homogeneity of nominal variables. See Figure 27.1(a) later inthis chapter.

The money demand variables do not necessarily enter in as simply as the moneysupply variables. For convenience, however, we will adopt a simple functional form for the money demand function, in which the demand for money is proportional to real income in the same way as it is proportional to the price level.3 Then Y and Y* will determine the exchange rate in simple ratio form. We also adopt the simplifyingassumption that the interest rates enter in simple difference form, represented by thefunction l ( ):

5 l (i 2 i*) (27.8)

The simpler functional form chosen for Equation 27.8 clarifies how the exchange ratedepends on Y, Y*, i, and i*.4 An increase in domestic real income, Y, has a negativeeffect on —that is, it causes the domestic currency to appreciate—and an increase inforeign income has the opposite effect. An increase in the interest differential, i 2 i*,has a positive association with —that is, it causes the domestic currency to depreciate.5

These effects are precisely the reverse of the effects that income and the interestrate appeared to have on the exchange rate in the Mundell-Fleming model in preced-ing chapters. The apparent contradictions merit some explanation.

First consider the effect of income. Recall exchange rate determination in theMundell-Fleming model. There an increase in income, Y, because it meant higherdemand for imports and a deteriorated trade balance, required a depreciation of the

S

S

M /M*Y /Y*

S

S

3In other words, the demand for nominal money balances is proportional to nominal GDP, which is PY. Thisassumption holds, for example, in the quantity theory of money, in which velocity, PY M, is constant. In thatmodel, however, money demand does not depend on the interest rate.

/

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currency.6 Equation 27.8 implies the reverse relationship with Y. The difference is thatthis section assumes that prices are perfectly flexible and that Y is therefore always atthe level of potential output, where all resources in the economy are fully employed.Think of Y as having a bar over it (like ) to indicate that it refers to potential output.In this context, if income increases, it is not because of expansionary monetary policyor any other kind of increase in demand, but because of supply-side factors such as ahigher level of national resources or an improvement in economic efficiency. In otherwords, when prices are perfectly flexible, all changes in output are changes in potentialoutput. When income increases because of such reasons, it is a sign of strength in theeconomy and tends to appreciate the currency because it raises the demand for money.For example, appreciation of the yen in the 1970s and 1980s was attributed to rapidgrowth in the Japanese economy. Appreciation of the dollar in the latter half of the1990s was attributed to rapid growth in the U.S. economy.

Now consider the effect of interest rates. In the Mundell-Fleming model (with par-tial capital mobility), an increase in the interest differential, because it improved thecapital account, required an appreciation of the currency. In Equation 27.8, in contrast,an increase in the interest differential is associated with a depreciation of the currency.It is important to see the reason for this difference as well.

From the covered interest parity condition, Equation 27.2, the forward discountcan be substituted in place of the interest differential. Furthermore, the uncoveredinterest parity condition, Equation 27.1, shows that the expected depreciation variablecan be substituted in place of the interest differential. We can rewrite Equation 27.8 asfollows:

5 l (Dse) (27.9)

An increase in the expected rate of depreciation of the currency, Dse, has a positiveeffect on today’s exchange rate (it causes the currency to depreciate today). It is clearwhy: If investors expect the domestic currency to lose value over the coming period,they will choose to shift their portfolios out of that currency and into other assets toprotect themselves against the expected future losses. When they seek to shift out ofthe domestic currency, they drive down its value today ( rises). There is an importantprinciple here. If expectations regarding what will happen in the future change, even ifno other variables change today, then today’s exchange rate will change. In this con-text, a high interest rate is not a sign of strength for a currency. Rather, it reflectsexpected future depreciation and is thus a sign of weakness.7 This is why a high (nomi-

S

M /M*Y /Y*

S

S


7When investors shift their portfolios out of domestic money in response to expectations of depreciation, whatdo they shift into? They shift into either domestic or foreign bonds. It makes no difference which, becauseunder the assumption of perfect substitutability, or uncovered interest parity, domestic and foreign bonds areessentially the same thing. In a different version of the model, the currency substitution model, people arethought to shift directly from domestic money to foreign money. However, unless they are planning on actu-ally traveling to the foreign country to buy goods, there is in reality little reason for them to hold foreignmoney. To do so would be to voluntarily give up the interest that could be earned on foreign bonds.

6In Problem 5 at the end of the chapter, you are asked to solve the balance-of-payments equilibrium condition(Equation 22.4) for S.

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nal) interest rate is not necessarily associated with a strong currency, as it is in theMundell-Fleming model.

So far, we have represented the rate of return variable (the opportunity cost ofholding domestic money) of Equation 27.8 in three ways: as the interest rate differ-ential, the forward discount, and the expected rate of depreciation. There is yet a fourth way to express the rate of return variable, and it will help clarify the first threeexpressions.

Equation 27.3 expressed purchasing power parity in terms of levels; but it can alsobe expressed in terms of rates of change:

D 5 Dp 2 Dp* (27.10)

where D is the annualized percentage rate of change of the exchange rate in long-runequilibrium, Dp is the domestic inflation rate, and Dp* is the foreign inflation rate.Equation 27.10 says that if the domestic inflation rate exceeds the foreign inflationrate, then the domestic currency depreciates at the rate of the inflation differential, toprevent the country’s goods from becoming overpriced in world markets.8

If the exchange rate acts according to Equation 27.10, investors are presumablyaware of this and form their expectations accordingly. Then expected depreciation isequal to the expected inflation differential.

Dse 5 Dpe 2 Dp*e (27.11)

In other words, investors expect the domestic currency to lose value to the extent thatthey expect its purchasing power over goods to deteriorate at a faster rate than for theforeign currency.

Observe that if the interest differential is equal to the expected rate of deprecia-tion (Equation 27.1, the uncovered interest parity condition) and the expected rate ofdepreciation is in turn equal to the expected inflation differential (Equation 27.11, PPPin rate of change form), then it follows that the interest differential is equal to theexpected inflation differential.

i 2 i* 5 Dpe 2 Dp*e

This can also be represented as the domestic real (that is, expected-inflation adjusted)interest rate equal to the foreign real interest rate.

i 2 Dpe 5 i* 2 Dp*e

This condition is called real interest parity.9

s

s


9Real interest parity could also be obtained through an alternative route—if the real interest rate in eachcountry were tied to a technological constant, the marginal product of capital. In practice, however, real inter-est rates are observed to be neither constant over time nor equal across countries at a point in time. (Again,only as a description of the long run is the flexible-price view of the world that provides real interest paritymeant to be taken literally.)

8Again, the empirical evidence in Chapter 19 showed that PPP is unlikely to hold in the short run. Remember,however, that the model in this section properly applies only to long-run exchange rate determination. Theshort-run deviations from the equation will be developed soon enough.

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Using Equation 27.11, we can substitute the expected inflation differential intoEquation 27.9.

5 l (Dpe 2 Dp*e) (27.12)

Now we see that investors will seek to shift out of a currency, thus causing it to depre-ciate, when it is expected to lose future value in the sense of a high expected rate ofinflation.

Venezuela is an example of a country with a high rate of inflation, as compared tothe United States.The Venezuelan inflation differential has held consistently enough inthe past that by now it is built into expectations and the interest differential. Japan is anexample of a country that has long had a low inflation rate, which has become similarlybuilt into its economy.Thus PPP states that the Venezuelan bolivar will depreciate overtime while the yen will appreciate over time. The monetary theory also states some-thing stronger, however. It states that when there is a sudden increase in expectedfuture inflation—for example, because a new, more expansionary head of the centralbank is appointed—the currency depreciates immediately.

Expectations of Money Growth

What determines the expected inflation rate? Many factors affect the inflation rate,especially in the short run. In the simple monetary model, however, the rate of moneycreation, exogenously set by the central bank, drives everything. This can be seen fromthe money market equilibrium condition, Equation 27.4. Remember that, becauseprices are perfectly flexible, income in the equation is tied to the exogenous level ofpotential output. Imagine that the inflation rate, although not zero, is in a steady state,that is, it is constant and has been fully incorporated into expectations and interestrates. It follows from Equation 27.4 that the given rate of increase of the price levelpresupposes a money growth rate of the same magnitude. If the money growth rate isexogenously set by the central bank, the inflation rate necessarily adjusts accordingly.The point can be made in terms of the LM curve used so extensively in the precedingchapters: If the money growth rate were not fully reflected in the inflation rate, that is,if the real money supply were increasing, then the LM curve would be shifting to theright and real income would be increasing. For there to be a steady state, the ratio ofthe money supply to the price level must be constant.

What is the effect on the exchange rate of a permanent increase in the moneygrowth rate of, say, 1 percent per annum? The inflation rate goes up permanently by 1 percent per annum.As soon as the change is recognized by the public, expected depre-ciation and the interest rate go up by the same 1 percent. As a result, the demand forthe currency falls. If the change is recognized at the same moment that it actually takeseffect, as it will be if the central bank announces the change in policy, then the price ofthe currency falls instantaneously. Figure 27.1(a) shows this as a discrete upward jumpin the exchange rate (and in the price level). This jump occurs even though the level ofthe money supply does not jump discretely, only its rate of growth does. Thus the per-

M /M*Y /Y*S


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centage change in the exchange rate in any given interval of time can be greater thanthe percentage change in the money supply observed during that interval (particularlyif the interval is short).This will happen if the change in the money supply is thought tosignal a permanent change in the per annum money growth rate.


FIGURE 27.1

The Effect of Changes in theMoney Supply on the EquilibriumExchange Rate

When the money supply, M, jumps to ahigher level, the equilibrium price level,P, and spot rate, , jump in proportion,as in (a). When the money supply growsat a faster rate, the equilibrium pricelevel and spot rate grow at the samefaster rate. In addition, there is a suddendrop in demand for the currency wheninvestors discover the change, as in (b).

S

M

(b) Rise in Money Growth

t0

P

t0

S

t0

M/P

t0

M

(a) Rise in Money Level

t0

P

t0

S

t0

M/P

t0

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Hyperinflation

An example where this framework, the monetary approach to the exchange rate, isthought to apply well is the case of hyperinflation. As we noted in Section 19.3, hyper-inflations occurred in a number of central European countries in the aftermath ofWorld War I. The German experience, from February 1920 to November 1923, hasbeen extensively studied. In October 1923 the rate of money growth reached 1,300 per-cent per month. The inflation rate reached 29,586 percent per month. That is just over20 percent per day; at that rate, the price level doubles in less than four days! Fascinat-ing stories abound of what life was like under such conditions. Wages were paid twice aday so workers could shop at lunchtime before prices rose again. So much paper cur-rency was needed to make simple purchases that a wheelbarrow might be needed tocarry it to the store. It is said that one shopper left a wheelbarrow full of cash briefly,and found on returning that the wheelbarrow had been stolen, but the currency hadbeen left.

In October 1923 the rate of depreciation of the mark reached 29,957 percent permonth.The price level and exchange rate were going up at roughly the same rate—thatis, the real exchange rate had reached a steady state. However, in the transition to thissteady state, the price level (and exchange rate) had gone up more than the moneysupply: Real money balances fell to a fraction (0.15) of their original level, as in the bot-tom panel of Figure 27.1(b).

Figure 27.2 illustrates the change in real money balances for thirteen hyperinfla-tions of the past century.The worse the hyperinflation, the more extreme the fall in realmoney holdings. This reflects the fact that the real demand for the currency dependsnegatively on the rate at which it is expected to lose value. Thus it is not quite true inthe new classical model that no change in a monetary variable can have an effect onany real variable. (We are classifying the level of real money balances as a real vari-able.) A change in the money growth rate has an effect on the level of real money bal-ances.10 Nevertheless, whether the change occurs in the level of the money supply or inits rate of change, there is still no effect on the real interest rate or real exchange rate.11

When the Money Supply Follows a Random Walk

The case already considered, where people expect a constant growth rate of domesticmoney indefinitely into the future, is relatively easy to understand. In this case, thevarious versions of the rate of return on alternative assets—the expected inflation dif-ferential, nominal interest differential, forward discount, and expected rate of depre-


11See Rudiger Dornbusch, “Lessons from the German Inflation Experience of the 1920s,” in R. Dornbusch,S. Fischer, and J. Bossons, eds., Macroeconomics and Finance: Essays in Honor of Franco Modigliani (Cam-bridge, MA: MIT Press, 1987), pp. 337–366.The seminal statement of the flexible-price version of the monetaryapproach to the exchange rate was made in the context of the German hyperinflation: Jacob Frenkel, “A Mon-etary Approach to the Exchange Rate: Doctrinal Aspects and Empirical Evidence,” Scandinavian Journal ofEconomics (1976): 200–224. The classic study of money demand in interwar hyperinflation is Philip Cagan,“The Monetary Dynamics of Hyperinflation,” in Milton Friedman, ed., Studies in the Quantity Theory ofMoney (Chicago: University of Chicago Press, 1956).

10This property is called a lack of “superneutrality.”

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ciation—are all equal to the expected money growth rate differential. The public’sexpectations as to the future path of the money supply in the long run, however, maynot be accurately described by a single constant growth rate. Consider two alternatives.

First, what happens if the money supply is thought to follow a random walk? Thatis, although people know the money supply will probably change, they think it could aseasily go down as up. At any point in time, the best forecast of the change in moneysupply is zero. As a matter of fact, there is indeed a great deal of “noise” in the monthlymoney supply numbers that are reported, for example, by the Federal Reserve. Thismeans that when the central bank reports an increase in the money growth rate in agiven month, the chances are good that the increase is purely transitory and does notsignal a new, permanently higher money growth rate.

If the expected values of the future money supply changes are zero, then theexpected inflation differential, expected depreciation rate, and interest rate differentialare also zero.12 The middle term disappears from the equations for derived earlier. AS


12Any increase in money demand coming from growth in potential output is omitted here. If money demandincreases, the currency can appreciate even without a change in the money supply. There also has long been agradual downward trend in real money demand arising from innovation in banking. For example, since theinvention of automatic teller machines, there has been less need to carry cash around.

FIGURE 27.2

Real Money Holdings in Great Hyperinflations of the Twentieth Century

Real money holdings fall in hyperinflations because the demand for money depends on expectedrates of return. The larger the increase in the inflation rate, the bigger the fall in real money.

Argentina '89Bolivia '85

Serbia '94

Hungary '23Russia '24

Germany '23

Zaire '93

Peru '90

Poland '23Austria '22

Brazil '90

Hungary '46

Peak monthly inflation rate

M/P

pea

k M

/P in

itial

10 10,000 10,000,0000.002

0.005

0.01

0.02

0.05

0.1

0.2

0.5

1

10,000,000,000 1016 10191013

Greece '44

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1 percent increase in the money supply, although it has a 1 percent effect on the pricelevel and exchange rate, has no further effects. This case is illustrated in Figure 27.1(a)for a single change in the money supply. The exchange rate simply follows a randomwalk in lockstep with the domestic money supply (relative to the foreign money sup-ply). Note that these are the only circumstances—random-walk money supplies in aflexible-price monetary model—under which the exchange rate should theoretically beexpected to follow a random walk. Most of the time there will be some reason toexpect future depreciation (or appreciation) over a long horizon, as in a high- (or low-)inflation country.

When the Money Supply Is Expected to Jump in the Future

What happens if the public suddenly raises its estimate of the probability that themoney supply will be increased in four years because the more expansionary of twopolitical parties will come to power in the next presidential election? Four years fromnow, assuming the anticipated increase in the money supply indeed materializes, theexchange rate will increase proportionately. It might seem that an event so far off inthe future would have no effect on today’s exchange rate. This supposition turns out tobe incorrect, however, assuming that investors’ expectations are forward looking, orrational. Under rational expectations, investors know the true model that determinesthe exchange rate. They form their expectations of the future exchange rate by takingthe mathematical expectation, using all available information including their knowl-edge of the true model. In other words, expectations, meaning what investors antici-pate, are now the same as mathematical expectation, meaning the average realizedvalue given all available information.13

Rational investors, in estimating how much the currency will be worth next period,will think further ahead in the future than just one period.They will make the followingcalculation.They will realize that if it is known that the money supply and the exchangerate will increase in year 4, then in year 3 investors will shift their portfolios out of thedomestic currency to protect themselves from the capital loss expected over the subse-quent period. They will realize that, as a result, some of the depreciation will take placein year 3. However, if it can be foreseen that the currency will depreciate in year 3, thenit can be foreseen that investors in year 2 will shift out of the domestic currency to pro-tect themselves from the expected loss; some of the depreciation thus takes place inyear 2. If the currency is expected to depreciate in year 2, by the same logic it willdepreciate in year 1. Finally, if the domestic currency is expected to depreciate in year1, then rational investors living in the present will shift their portfolios out of it immedi-ately. If all today’s investors make this calculation, they will cause the currency todepreciate today, even if the money supply is not expected to increase for four years.


13Chapter 26 explained that workers who have rational expectations forecast the price level optimally anddetermine their wage demands accordingly. Here investors who have rational expectations forecast theexchange rate optimally and determine their asset demands accordingly. In both cases, the individuals areassumed to have as much knowledge of the correct model of the economy, and as much up-to-date informa-tion on the economic variables, as the economists building the model.

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In theory, if investors suddenly decided for some reason that the money supplywas going to increase in the year 2100, by the same logic there would be an effect ontoday’s exchange rate. The effect on today’s exchange rate is smaller, the further intothe future is the expected increase in the money supply. Future changes in the moneysupply are discounted back to the present. So, reassuringly, the anticipation of anincrease in the money supply in the year 2100 would have a negligibly small effect onthe exchange rate today.

27.3 Two Examples of the Importance of Expectations

The expectation regarding future changes in the exchange rate plays a key role, as wehave seen. We further offer two specific illustrations of this point, while staying withinthe framework of the same model.

Speculative Bubbles

Exchange rates are often alleged to fluctuate excessively, in the sense that “unneces-sary” movement in the exchange rate takes place even in the absence of any movementin fundamental macroeconomic variables such as the money supply. We have just seenin the preceding section that today’s exchange rate can move in a given period withoutany movement in the money supply taking place in that period. This is not a validexample of excess variability, however, because such movements are caused by expec-tations of actual movements in the money supply, even if the latter do not take place in the same period. The question arises whether changes in expectations that shiftdemand for the currency and thus cause the exchange rate to move can occur with nobasis in fundamentals at all.

Financial commentators have discussed the possibility of speculative bubbles eversince such classic historical episodes as the Dutch tulip bulb mania of the seventeenthcentury and the South Seas Company stock market bubble of the early eighteenth cen-tury, which even took in Sir Isaac Newton. In recent years, large puzzling movements inexchange rates have been identified as speculative bubbles by some. The final 20 per-cent appreciation of the dollar in the eight months preceding its peak in 1985, forexample, seems difficult to explain otherwise. (Refer ahead to Figure 27.4(b).) Thesame is true of the appreciation of the yen up to 1995.

When the exchange rate is on a speculative bubble path, it wanders away from theequilibrium value dictated by macroeconomic fundamentals because of self-confirmingexpectations. Such a bubble would arise as follows. In period 0, speculators suddenlydecide for some reason that the currency is going to depreciate in period 1. (For exam-ple, even without any good reason to expect a future change in fundamentals, specula-tors may form their expectations by simplistically extrapolating a recent blip in theexchange rate.) To protect themselves against the feared depreciation, they sell the cur-rency and drive down its price in period 0. Is such behavior irrational? Not necessarily.The currency might actually depreciate in period 1, justifying their fears; it will do so ifthere is a fall in demand for it in period 1, which will happen if there is an expectation

27.3 ■ Two Examples of the Importance of Expectations 585

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of further depreciation in period 2. Is it irrational to expect a depreciation in period 2?Not if there is a fall in demand for it in period 2 because of an expectation of deprecia-tion in period 3. Similarly, it will be rational to expect depreciation in period 3 if depre-ciation is also expected in period 4, and so forth. If there is an ultimate day of reckoningon which the value of the currency is known to be tied down to some specific value, thiswill prevent the speculative bubble from getting started. But without such a day ofreckoning, there is nothing in the expectations logic that prevents the exchange ratefrom soaring indefinitely high, regardless of the economic fundamentals. Althoughsociety in the aggregate will probably be harmed by such unnecessary movements, eachindividual speculator will feel constrained to follow the herd because, given that every-one else is pushing the exchange rate up, the individual would lose money by trying tobuck the trend alone.

In practice, the exchange rate does not shoot off to infinity, that is, diverge indefi-nitely far from the long-run value implied by fundamentals. At most, it wanders awayfrom fundamentals equilibrium for a short time before the bubble bursts. It is possible,however, that such bubbles regularly form and subsequently burst, thus adding to thevariability of floating exchange rates. Some of those who believe this phenomenon isimportant argue that a more interventionist policy on the part of the government mightbe able to reduce unnecessary volatility in the economy even without a change in mon-etary policy.

Target Zones and the Honeymoon Effect

Some economists who dislike the high variability of floating exchange rates, but whorecognize that fixed exchange rates are not a practical alternative for large industrial-ized countries, propose the adoption of a system of target zones for the dollar, yen, andEuropean currencies. Under this system the countries involved would (1) agree on the fundamental equilibrium value of each exchange rate (subject to periodic review),(2) agree on fairly wide bands within which exchange rates would be free to fluctuate,and (3) commit to altering monetary policies when exchange rates threaten to violatethose bands.14 Critics of such schemes object on the basis that governments are notvery good at choosing the correct fundamental equilibrium rates.

The theory of target zones shows—when the authorities are credibly committed tousing monetary policy to stabilize the exchange rate within the announced bands—thatspeculation can help in this effort. The theory was developed in the 1980s to describethe Exchange Rate Mechanism of the EMS.15 Let us assume that France and Germanyannounce that the franc mark rate will be subject to specified margins around the cen-tral rate, say plus or minus 21⁄4 percent. (This was the actual width of the band from 1979to 1993. Denmark still maintains such a band.) What happens if, subsequently, French

/


15Paul Krugman, “Target Zones and Exchange Rate Dynamics,” Quarterly Journal of Economics, 106 (1991):669–682.

14John Williamson, “Target Zones and the Management of the Dollar,” Brookings Papers on EconomicActivity, 1 (Washington, DC: Brookings Institution, 1986): 165–174.

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or German economic fundamentals drift in a particular direction and the exchangerate draws near to one of the proclaimed margins of the target zone?

The horizontal axis of Figure 27.3 measures economic fundamentals. Assume thefranc mark rate is determined by the monetary model, as represented by Equation27.9, so that fundamentals are represented simply by (M M*) (Y Y*). The verticalaxis measures the franc mark exchange rate, S. Let us say that the exchange rate nearsthe upper margin because real growth in Germany exceeds real growth in France. Ifthe monetary authorities do not have a genuine commitment to the target zonearrangement, then there is nothing to stop the exchange rate from going right throughthe boundary. But let us assume the authorities are in fact prepared to adjust monetarypolicy to keep the exchange rate inside the band. This means that the Bank of France isprepared to reduce French money growth to offset the decrease in the relative demandfor francs.

It might appear that as soon as the macroeconomic fundamentals, (M M*)(Y Y*), reach the level of 21⁄4 percent above the central rate, where the diagonal linecrosses the upper margin for S at point D1, the Bank of France must step in to preventthe rate from breaching the limit. But we must remember that the exchange rate isdetermined not just by the current fundamentals but also by investor expectations, Dse.When the exchange rate nears the upper margin, speculators are aware that it is much

///

////

/

27.3 ■ Two Examples of the Importance of Expectations 587

FIGURE 27.3

The Target Zone

If expectations played no role, then the monetary authorities would have to intervene as soon asfundamentals had drifted as far as 62 percent, at D1. But speculation helps reduce the range ofvariation of S.

1/4

Uppermargin

Centralrate

–Z%

S1

S2

S3

D3

D1

–21/4%

–21/4%

+Z%+21/4%

+21/4%

Exchangerate

FundamentalsM/M*Y/Y*

0+

+––

Targetzone

Lowermargin

Honeymooneffect

Honeymooneffect

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more likely in the future to move down rather than up because the central bank willintervene against an upward movement. In other words, Dse is negative. Investorsrespond with a reduced demand for marks. The result is that when fundamentals are atD1, the equilibrium value of the exchange rate is at S1. Thus speculation works to nar-row the range of variation of the exchange rate, even before the authorities roll uptheir sleeves. The difference between the two points has been called the honeymooneffect. Not until the fundamentals reach some more extreme limiting point, indicated inFigure 27.3 by 1Z%, will the exchange rate draw so close to the boundary of the targetzone that the Bank of France is forced to intervene by taking francs out of circulation.This is point S2.

The same honeymoon effect holds at the lower margin. If the fundamentals drift to21⁄4 percent below the central rate, speculators know that a future increase is morelikely than a future decrease. They respond by increasing their demand for marks. Theypush the exchange rate up from point D3 to point S3. The honeymoon effect pushesother points off the diagonal line as well, into a curve with a flattened S shape. The keypoint is that speculation helps narrow the range of variation. The catch, once again, isthat the authorities’ commitment to intervene when necessary must be credible.

27.4 Overshooting and the Real Exchange Rate

The equation developed in Section 27.2 has a number of problems if it is intended as acomplete theory. Chief among them is that it at best explains only movement in thenominal exchange rate. As a consequence of the flexible-price, or PPP, assumption, itcannot account for movement in the real exchange rate. Chapter 19 showed that theevidence is strongly against PPP—in other words, against a constant real exchangerate—in the short run. It appears that goods prices are in fact sticky, whether as a resultof imperfect information, contracts, costs incurred in changing prices, or inertia in con-sumer habits. As a result, disturbances in the nominal exchange rate are reflected asdisturbances in the real exchange rate, which die out only very slowly over time. Thiswas the justification for the constant-price assumption made in the Keynesian andMundell-Fleming models (Chapters 17–18 and 22–23, respectively). Assuming thatgoods prices are literally constant is too extreme, however. In the presence of excessdemand for goods, prices do eventually adjust upward. The flexible-price monetarymodel went to the opposite extreme and assumed there are no barriers to preventgoods prices from adjusting instantaneously. This section develops the sticky price ver-sion of the monetary model. It is a realistic synthesis of the two extremes. It turns outto be equivalent to the Mundell-Fleming model in the short run and the monetaristmodel in the long run. The model is from a classic article by Rudiger Dornbusch.16

The effort to derive the long-run equilibrium exchange rate, , in the first half ofthe chapter has not been wasted. This section merely adds in S 2 , short-run devia-tions of the exchange rate from that equilibrium.

SS


16“Expectations and Exchange Rate Dynamics,” Journal of Political Economy (1976): 1161–1174.

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International Differences in Real Interest Rates

Related to the problem that real exchange rates are not constant is the problem thatreal interest rates also are not constant. National differences in nominal interest ratesdo not fully reflect differences in expected inflation rates. In the 1970s there was arough correspondence between interest rates in the major industrialized countries andtheir inflation rates. Those countries that experienced substantial increases in inflationalso experienced substantial increases in nominal interest rates. Thus the pattern of the1970s was loosely consistent with the idea that nominal interest rate differentialsreflect expected inflation differentials. In other words, the pattern was consistent withthe real interest parity condition used to derive Equation 27.12.

This pattern broke down after 1980. Nominal interest rates rose in all countriesand came down only slowly after 1984, even though inflation began declining steadilyin 1981. The U.S. interest rate rose the furthest, even though inflation in the UnitedStates fell more rapidly than in Japan and Germany. In the early 1990s the situationreversed: The real interest rate in Germany rose above the U.S. real interest rate. Inshort, real interest differentials became large and highly variable in the 1980s and1990s.17 For this reason, the models cannot remain in the simple form that assumes realinterest parity. Variation in the real interest rate differential must be included as anadditional factor in the model of variation in the real exchange rate.

We retain the assumption that expected returns are equalized across countrieswhen expressed in common currency units: Not only are there no barriers that slowdown portfolio adjustment, but investors treat domestic and foreign bonds as perfectsubstitutes in their portfolios.18 Thus uncovered interest parity holds as before.

i 2 i* 5 Dse

Subtracting the expected inflation differential, Dpe 2 Dp*e, from both sides yields ananalogous parity condition in real terms:

(i 2 Dpe) 2 (i* 2 Dp*e) 5 Dse 2 Dpe 1 Dp*e

or

r 2 r* 5 (Dsreal)e (27.13)

27.4 ■ Overshooting and the Real Exchange Rate 589

18Saying that expected rates of returns are equalized across countries when expressed in common units is notthe same as saying that real interest rates are equalized across countries. A country’s real interest rate is thereturn on its bonds, expressed in terms of purchasing power over that country’s goods. An internationalinvestor has an incentive to arbitrage away any differentials in interest rates when expressed in a common cur-rency, but there is no incentive to arbitrage away a differential between the U.S. rate of return expressed interms of U.S. goods and the German rate of return expressed in terms of German goods. If PPP held, then thetwo calculations would be the same. However, this section allows for the fact that PPP does not hold.

17One can sometimes come to different conclusions regarding real interest rates, depending on the precisemeasure one uses for expected inflation. The apparent variation in real interest rates in the 1970s was smallenough that some economists attributed it entirely to the problem of measurement, believing that, ex ante, realinterest rates were, in truth, constant. But movements in the 1980s were so large, regardless of what measureone uses for expected inflation, that it was no longer possible to argue that real interest rates were constant.Real interest rates for the United States and an average of ten trading partners are shown in Figure 27.4(a).

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where r and r* are the domestic and foreign real interest rates, and (Dsreal)e is theexpected rate of change of the real exchange rate, SP* P, algebraically equal to theexpected rate of change of the nominal exchange rate minus the expected inflation dif-ferential. Equation 27.13 shows that the differential in real interest rates is equal to theexpected rate of real depreciation of the currency. Intuitively, if investors expect acountry’s currency to be depreciating in real terms, they will not be willing to hold itsassets unless they are compensated by a higher real interest rate.

To take an example, we have noted that in 1984–1985 the U.S. real interest rate wasabove its major trading partners’ real interest rates. We now see that this differentialwas signaling that investors expected the dollar to depreciate in real terms in thefuture. (They turned out to be right.) To take a different example, Chile had very highreal interest rates in the late 1970s, signaling in part that investors considered the gov-ernment’s attempt to peg the value of the currency at a high level to be unsustainable.(They too turned out to be right.)

Regressive Expectations

The next question is what determines expectations. It is always difficult to modelexpectations because it is difficult to know what goes on inside people’s minds. Yet it isnatural to suppose that, when the exchange rate is observed to deviate from the long-run equilibrium level, investors will expect it to move back in the direction of that equi-librium over time. For this purpose we need to know what we mean by the long-runequilibrium. PPP is a good candidate for the long-run equilibrium. In fact, we used theassumption of PPP in the monetary model at the beginning of the chapter to representthe long-run equilibrium level of the exchange rate, .

Section 19.2 showed that after a disturbance there is a slow but positive tendencyfor the real exchange rate to return toward PPP until the next disturbance comesalong. The tendency to return to equilibrium is so slow—and new disturbances comealong so often—that it is difficult to detect. When a large enough data sample is exam-ined, however, it is possible to detect a tendency for the exchange rate to eliminate 15 percent or more of the existing gap per year. If this tendency to regress toward equi-librium exists in the real exchange rate, then investors are presumably aware of it. (Thisis another application of the idea that investors are rational.) Thus investors are said tohave regressive expectations:

Dsereal 5 2u(S 2 ) (27.14)

The equation says that when the currency is thought to be overvalued, that is, to have ahigher current value than is given by long-run equilibrium, , investors will expect it todepreciate in the future. When the currency is thought to be undervalued, that is, tohave a lower current value than in long-run equilibrium, investors expect it to appreci-ate in the future.The parameter u is the rate at which the real exchange rate is expectedto regress toward equilibrium.

Before proceeding with Equation 27.14, it would be reassuring to have some evi-dence that this is, in fact, how expectations are formed. A number of surveys periodi-cally ask bankers, foreign exchange traders, economists, and other market participantstheir expectations regarding the exchange rate. Although different survey respondents

S

S/S

S

/


CAVE.6607.cp27.571-606 6/6/06 1:38 PM Page 590

form their expectations in different ways, some systematic patterns are evident. Afterthe dollar appreciated sharply above its PPP level in the early 1980s, for example, thesurvey respondents reported an expectation that it would depreciate in the future.According to two surveys, the median investor in 1984 expected the dollar to depreci-ate at a rate of 8.5 percent to 10.0 percent over the following year, against an averageof the mark, yen, pound, French franc, and Swiss franc.19 Equation 27.14 turns out to fitthese data well; the parameter u is estimated at 0.2. It is often dangerous to put toomuch faith in responses to surveys. In this case, however, it is reassuring that the speedat which people seem to expect the exchange rate to regress to PPP is in the generalrange of estimates of the speed at which it does in fact regress to PPP.

The Effect of Monetary Policy on the Real Interest Rate and Real Exchange Rate

We now combine Equations 27.13 and 27.14

r 2 r* 5 2u(S 2 )

and solve for the exchange rate as a function of the real interest differential.

(S 2 ) 5 2(1 u)(r 2 r*) (27.15)

Equation 27.15 says that when the domestic real interest rate exceeds the foreign rate,the value of the domestic currency exceeds its long-run equilibrium value. Why?

Consider an increase in the Canadian real interest rate, as for example occurred inthe 1988–1990 monetary contraction. It quickly leads to an increase in internationalinvestors’ demand for Canadian assets, causing the Canadian dollar to appreciate.When the currency appreciates above its long-run equilibrium value, investors expectthat in the future it will have to come back down because it is overvalued. How muchdoes the currency appreciate? Until it has gone far enough that the expectation offuture depreciation back toward equilibrium is large enough to offset the interest dif-ferential. Only then will investors be willing to hold other assets despite the fact thatthey do not pay as high an interest rate as Canadian assets. In other words, the overval-uation must be sufficiently large to offset the interest differential in the minds ofinvestors. Loosely speaking, capital comes into the country and the currency appreci-ates until this condition is met. More precisely, the appreciation should be simultane-ous with the increase in the interest rate and the resulting increase in demand fordomestic assets. No measurable net capital inflow need actually take place. Recall thatthe exchange rate adjusts instantaneously so as to equate supply and demand.

Notice in Equation 27.15 that if u is large, the coefficient (1 u) is small. A givenincrease in the real interest differential will be associated with only a small appreciationof the currency because this is sufficient to generate the necessary expectation of futuredepreciation. If the expected speed of adjustment is low, however, then the effect on the

/

/S/S

S/S


19This is as contrasted with the average for the period 1976 to 1979, before the dollar appreciation had begun,when expected depreciation was 20.2 percent. Jeffrey Frankel and Kenneth Froot,“Using Survey Data to TestStandard Propositions Regarding Exchange Rate Expectations,” American Economic Review, 77, no. 1 (1987):133–153.

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exchange rate can be large. For example, if u is 0.2, then a .01 increase in the real inter-est rate causes a 5 percent (.01 0.2) appreciation of the currency.

Let us return to the example of the shift in U.S. monetary policy that took place in1979. In the late 1970s monetary policy had been loose in the United States and theinflation rate was high. As a result, real interest rates became low, even below zero.(Although nominal interest rates were relatively high by historic standards, the infla-tion rate was just as high.) Figure 27.4(a) shows how low U.S. real interest rates were inthe late 1970s. In this period the dollar depreciated to what was then its lowest level ofthe floating rate era.Then, in October 1979 the Federal Reserve Board under ChairmanPaul Volcker dramatically shifted monetary policy to a tighter stance to fight inflation.Interest rates rose sharply in early 1980, and the dollar appreciated in response to theincreased attractiveness of U.S. assets. The nominal interest rate differential betweenthe United States and its trading partners, approximately zero in the period 1976 to1979, rose to about .03 in the period 1981 to 1982.

The real interest rate differential continued to rise through mid-1984, mostly in theform of declining expectations of U.S. inflation. The rise was clear for long-term inter-est rates, shown in Figure 27.4(a). The increase in real rates of return made U.S. assetsmore attractive and caused the dollar to appreciate. Figure 27.4(b) shows how the realvalue of the dollar increased with the real interest rate differential. As of mid-1984, areal interest rate differential as large as 3 or 4 percent on ten-year bonds implied thatinvestors expected the dollar to depreciate in real terms at a rate of at least 3 percentper year on average over the next ten years, or 30 percent altogether. If ten years isconsidered the appropriate length of time needed for the real exchange rate to returnvirtually all the way to its long-term equilibrium level, then this simple calculation sug-gests that investors considered the dollar to be about 30 percent above its long-runequilibrium.20

In terms of the Mundell-Fleming graph, the U.S. economy in the mid-1980s couldbe represented as an IS-LM intersection at a real interest rate in excess of that prevail-ing in the rest of the world. The reason has been discussed before: an imbalanced mixof monetary and fiscal policy. Chapter 23 raised the question of how a positive realinterest differential like this could be consistent with perfect capital mobility. Now weknow the answer: Because the dollar had appreciated so far above its long-run equilib-rium, there was an expectation of future dollar depreciation that was sufficient to off-set the interest differential in investors’ minds.

Long-Run Equilibrium

We have shown that the level of the exchange rate, S, relative to its long-run equilib-rium, , is determined by the real interest rate differential, itself determined by suchfactors as monetary policy. If is constant, for example, movement in S is entirelyS

S

/

20The argument for looking at long-term real interest rate differentials to see how overvalued the market con-siders the currency to be was developed by Peter Isard, “An Accounting Framework and Some Issues forModeling How Exchange Rates Respond to the News,” in Jacob Frenkel, ed., Exchange Rates and Interna-tional Macroeconomics (Chicago: University of Chicago Press, 1983).

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FIGURE 27.4

U.S. and Foreign Real Interest Rates and the Exchange Rate

(a) The U.S. real interest rate was low in the late 1970s and high in the early 1980s, bothabsolutely and relative to Group of 10 trading partners. (b) The big swings in the real interestdifferential usually coincide with swings in the value of the dollar.

(a) Nominal and Real Long-Term Interest Rates

U.S. nominal

U.S. real

Foreign (G-10) real

25

Percentage(yearly)

20

15

10

5

0

�10

�5

1974 19781976 1980 1982 1984 1986 1988 1990 1992 19961994 1998 2000 2002 2004 2006

1974 19781976 1980 1982 1984 1986 1988 1990 1992 19961994 1998 2000 2002 2004 2006

(b) The Dollar and Real Interest Rates

Long-term realinterest ratedifferential(left scale)

CPI–adjusted dollaragainst G-10 countries(right scale)

160

Index, January 2000 � 100(monthly)

Percentage(yearly)

140

120

100

80

�4

�2

2

0

4

6

8

10

60

CAVE.6607.cp27.571-606 6/6/06 1:38 PM Page 593

explained by movement in the real interest rate differential. In general, however, it isunlikely that the long-run equilibrium rate is constant. Even assuming that the long-run equilibrium real exchange rate is constant,21 it cannot be assumed that the equilib-rium nominal exchange rate, , is constant. Because it is a nominal magnitude, like theprice levels, it will follow a rising path over time in an economy with a high rate ofmoney growth and inflation.

Section 27.2 used PPP to derive a model of the exchange rate. At that point wewere operating under the assumption that prices were perfectly flexible, whereas wehave recognized since then that they are in fact sticky. In the long run, prices are flexi-ble, however. Thus PPP can be used to characterize long-run equilibrium. So, althoughEquation 27.12 no longer serves as a model of the moment-to-moment exchange rate,S, it now serves nicely as a model of the long-run equilibrium exchange rate, .

The next task is to see how the exchange rate moves from the short-run equilib-rium to the long run. The transition from short run to long run is illustrated in Fig-ure 27.5, which shows the exchange rate on the horizontal axis and the price level onthe vertical axis. The proportionality between and P that holds in PPP equilibrium isgraphed as an upward-sloping 45º line. It is necessary to be on the PPP line only in thelong run. This means that when the money supply goes up permanently by 10 percentand the price level eventually rises proportionately, the exchange rate too will eventu-ally rise by the same 10 percent. This is a movement up along the PPP line, from pointA to point B.

Equation 27.15 indicates that in the long run, with the exchange rate at its equilib-rium level (S 5 ), the real interest rate differential is zero (r 5 r*). The explanation isthat if there is no reason for investors to expect future depreciation of the currency (inreal terms), then they have no reason to require a (real) interest rate differential to bewilling to hold the currency. This international equalization of real interest rates is sim-ilar to the real interest parity condition that followed from Equation 27.11 in Section27.2, but now we see that it holds only in long-run equilibrium.

The Path from Short-Run Overshooting to Long-Run Equilibrium

The central question addressed by the overshooting model is: What happens in theimmediate aftermath of an increase in the money supply? It would clearly be wrong toassume that the economy will stay on the PPP line; goods markets do not adjust fastenough to guarantee this in the short run. The assumption that goods prices are stickymeans that when the nominal money supply, M, increases by 10 percent, the realmoney supply, M P, on impact, also increases by 10 percent, because prices do notmove at all in the short run. Money market equilibrium then requires that the mone-tary expansion will drive down the interest rate. (In terms of the Mundell-Fleming

/

S

S

S

S


21The possibility that the long-run equilibrium real exchange rate might itself change cannot be ruled out.Japan long had an upward trend in the long-run equilibrium real value of its currency. To take another exam-ple, it has been suggested that the long-run equilibrium real value of the dollar is lower than it was in the 1980sbecause the United States has run up $3 trillion in international debt, which requires a permanent improve-ment in the trade balance to earn the foreign exchange to service the debt.

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model, the LM curve shifts to the right.) The lower interest rate in the home country, inturn, causes international investors to head for the exits. The decline in demand fordomestic assets causes the currency to depreciate.

We can figure the size of the depreciation. alone increases by the same 10 percentas the money supply. But the total change in S is greater: Equation 27.15 says that Sincreases by (1 u) times the fall in the interest rate.22 Only when the currency has depre-ciated that far do investors have the necessary expectation of appreciation back towardlong-run equilibrium that they must have if they are to hold domestic assets willingly,despite the fact that these assets pay a lower rate of interest than foreign assets.We havejust derived the now-classic overshooting result of Rudiger Dornbusch: Even thoughthe long-run equilibrium exchange rate increases by the same proportion as the moneysupply, the short-term equilibrium exchange rate increases more than proportionately.

/S/

S


FIGURE 27.5

The DornbuschOvershooting Diagram

An increase in the moneysupply, M, raises the pricelevel, P, and spot rate, S,proportionately in the longrun by PPP (at B). In theshort run, however, P istied down. As a result, S increases more thanproportionately in theshort run at C; that is, it overshoots its long-runequilibrium.

A A ′ CP = P

PPP : S = P/P*

B

Proportionalto ∆ M

Proportionalto ∆ M Overshooting

S S ′ S ′

P

P ′

P

S0

22The fall in the nominal rate is in turn 1 m times the increase in the money supply, where m is the semielas-ticity of money demand with respect to the interest rate. (See the chapter supplement.)

If the monetary expansion raises the level of output, then the interest rate will not fall by as much as itwould if the level of output were constant. As a result, the currency will not overshoot its long-run equilibriumby as much. Conversely, if the monetary expansion raises the expected inflation rate, then the real interest ratewill fall by more than the nominal interest rate, and as a result the currency will overshoot its long-run equilib-rium by more. But this does not qualitatively change the results described in the text. The algebra for thesecases, and indeed for this entire section, can be found in Rudiger Dornbusch, “Expectations and ExchangeRate Dynamics,” Journal of Political Economy, 84, no. 6 (1976), 1161–1176.

/

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Where is the economy now in Figure 27.5? In the short run it cannot leave the hor-izontal latitude of the starting point, A, because P is tied down. S increases, whichmeans a move to the right in the graph. How far? The economy moves further thanpoint A9 because if it stopped there, S would have increased only by the same percent-age as . S must increase by more than . Thus the economy moves, on impact, to apoint like C.23

Establishing the short-run equilibrium, C, and the long-run equilibrium, B, promptsthe next question: How do we get from here to there? At point C several factors arestimulating the demand for goods. First, the real interest rate has fallen, which shouldstimulate the domestic demand for capital goods, construction, and consumer durables.Second, the real value of the currency has fallen. Indeed, any point below or to the rightof the PPP line is a point where domestic goods are cheaper than foreign goods. Thisshould stimulate the demand for domestically produced tradable goods, such as the for-eign demand for exports. The increased demand for goods will put upward pressure onprices.The price level will be somewhat higher after a little time has passed.

As the price level, P, slowly rises to higher levels, the real money supply, M P,slowly declines to lower levels, although it is still higher than it was before the increasein M. (The LM curve slowly shifts back to the left.) As a result, the interest rate slowlyrises, although it is still lower than the foreign interest rate. Equation 27.15 shows thatas the interest rate rises, the currency appreciates back toward its long-run equilibrium;international investors no longer find domestic assets quite so unattractive. Thus, as wemove up in Figure 27.5 (higher P), we also move back to the left (lower S).24

The process continues as long as the real money supply is greater than it wasbefore the monetary expansion—that is, as long as the real interest rate and real cur-rency values are low—because the excess demand for goods continues to cause pricesto rise.When the price level has risen by the same proportion as the money supply, thenthe real money supply, real interest rate, and real exchange rate are all back to theiroriginal levels. Only then is there no excess demand for goods and no need for prices tocontinue rising. This long-run equilibrium is none other than point B, the PPP point atwhich all nominal magnitudes have increased by the same percentage. This illustrates ageneral principle that has recurred over several previous chapters: In the long run inwhich all real magnitudes have had time to return to their equilibrium values, all nomi-nal magnitudes must change proportionately. Figure 27.6(a) shows how, after the initialovershooting caused by the increase in the level of the money supply, the real moneysupply and real interest rate return over time to their original levels, and as a conse-quence the exchange rate gradually approaches its new equilibrium level.

Notice the correspondence between what investors at point C thought would hap-pen in the future and what actually did happen. In the short-run overshooting equilib-rium at C (when the price level had not yet had time to adjust to the increase in the

/

SS


23Point C corresponds to point B in the Mundell-Fleming diagram, Figure 23.3. The interest differential is nowattributed to the expectation of future appreciation (rather than to imperfect capital mobility).24The downward-sloping line connecting points B and C represents equilibrium in the asset markets, therelationship that must hold between P and S (via the interest rate, i) for the given money supply, M, to be will-ingly held.

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money supply), investors thought the currency would appreciate in the future becausethey had regressive expectations. We have just established that this is, in fact, what hap-pens as the price level adjusts: S does indeed move in the direction of . If investorshave rational expectations, then they know the complete model, and the rate at whichthey expect S to move toward is precisely the rate at which it does so.S

S


FIGURE 27.6

Overshooting Effects ofChanges in the Money Supply

(a) After a jump in the level of themoney supply, P can only increaseslowly. As a result, the real moneysupply M P, real interest differential,r 2 r*, and spot rate, S, temporarilydeviate from their long-run equilib-riums. (b) An increase in the rate ofchange of the money supply causessimilar deviations from long-runequilibrium, but now equilibrium is itself a moving target.

/

M

(a) Rise in Money Level

t0

P

t0

M/P

t0

SS

S

t0

M

(b) Rise in Money Growth

t0

P

P

t0

M/P

t0

S

t0

P

r – r*

t0

r – r*

t0

S

S

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The model studied at the beginning of this chapter, where goods prices were per-fectly flexible, can be viewed as a special case of the complete model. It is the casewhere adjustment in the goods markets is instantaneous. If the rate of change of pricesis highly responsive to the excess demand for goods, then the system will move to pointB very quickly. In the limit, the system will jump from A to B instantaneously. In thatcase, PPP always holds, S 5 , and Equation 27.12 constitutes a complete analysis ofexchange rate determination. The Mundell-Fleming model can be viewed as the oppo-site extreme, where the speed of adjustment in goods markets is very slow.25

Exchange Rate Volatility

We have seen what happens in the aftermath of a single monetary disturbance. How-ever, in practice, if one looks for the nominal exchange rate to follow the path of Fig-ure 27.5 in the aftermath of an overshooting episode—a smooth return to long-runequilibrium—one is likely to be disappointed. In the real world, new disturbancescome along all the time, so that before the exchange rate has had time to return muchof the way toward its equilibrium, a new policy change in one direction or the other islikely to occur.26 The effect on the exchange rate of any given monetary disturbance isas we have just seen it to be, notwithstanding the possibility of future disturbances.When each new change in the money supply hits, the exchange rate changes more thanproportionately; it then begins to move gradually back toward its long-run equilibrium,until the next monetary disturbance comes along.

Empirically, changes in the exchange rate are more variable than changes in themoney supply or the price level. It is an attractive property of the overshooting modelthat it can explain this variability in exchange rates without having to appeal to specu-lative bubbles or irrationality on the part of investors. The volatility of exchange ratesin the model is a consequence of the fact that asset markets adjust instantaneouslywhile good markets adjust slowly. If goods prices adjusted instantaneously, there wouldbe no overshooting of the exchange rate. Exchange rate changes would be no morevariable than changes in the money supply.

There is an analogy with a law of chemistry called Le Châtelier’s principle. Whenone variable in a physical system (such as the pressure or temperature of a gas) is con-strained from changing in response to a disturbance (such as a change in its volume),one or more of the other variables in the system must change by more than it other-wise would, to compensate. Paul Samuelson first pointed out the possible applicationto economics: When one price is constrained from changing in response to a change insupply of a commodity, some other price must change by more to compensate. WilliamBranson has pointed out the relevance for overshooting of the exchange rate: Whenthe general price level is constrained from changing in response to a change in themoney supply, the exchange rate changes more than proportionately to compensate.

S


26Refer back to Figure 19.3 for an idea of the frequency of disturbances to the real exchange rate in 200 yearsof U.S.–U.K. history.

25This discussion of overshooting has considered only changes in the level of the money supply. Changes in theexpected growth rate of the money supply also cause overshooting, as illustrated in Figure 27.6(b).

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27.5 ■ Two More Examples of the Importance of Expectations 599

Furthermore, the slower is the speed of adjustment (expected by investors), u inEquation 27.14, the greater is the degree of overshooting.27 This happens because if thespeed of exchange rate adjustment, u, is low, then for any given fall in the interest dif-ferential, it takes a large undervaluation of the exchange rate to generate the necessaryexpectation of future appreciation equal to the interest differential. In terms of Fig-ure 27.5, if u is low, the asset market equilibrium line is flat and the exchange rate has toincrease even further than C before investors are willing to hold domestic assets. If theexpected speed of adjustment is very high, however, then a movement just slightlybeyond A9, an increase in S just a little more than proportionate to the increase in themoney supply, will be sufficient to satisfy investors.

Without knowing precisely the size of u (or the other parameters in the monetarymodel), we cannot say the observation that exchange rates are much more variablethan money supplies necessarily means that exchange rates are excessively variable.The variability may simply be the overshooting phenomenon in operation.

27.5 Two More Examples of the Importance of Expectations

We have emphasized throughout this chapter the important role that expectations playin determining exchange rates in modern asset markets. We illustrate the point withtwo more examples.

The Example of Official Announcements of Economic Statistics

Government announcements illustrate the importance of changes in expectations. Con-sider the case of the weekly money announcements. Every week, the Federal ReserveBoard announces what the money stock was in the preceding week. In the early 1980sthe announcements were made at 4:10 p.m. on Friday afternoons and referred to themoney stock nine days earlier. The financial markets looked forward to each week’sannouncement with both eagerness and trepidation. When the time drew near, tradingslowed down and even stopped as traders gathered around the newswire or computerterminal. When the announcement came out, prices in the various financial marketswould jump in reaction, and trading would take off again. The most widely remarkedreaction took place in the credit markets. When the Fed announced a money supplythat was greater than observers had previously been expecting, interest rates wouldimmediately jump up in reaction (or bond prices would jump down, which is anotherway of saying the same thing).28 When the Fed announced a money supply that wassmaller than had been expected, interest rates would fall in reaction.

27The expected speed of the rate of exchange rate adjustment, u, in turn depends on the actual speed of adjust-ment of goods prices, assuming that expectations are rational.28Bond prices move inversely with the interest rate. If the interest rate is 5 percent, then a one-year Treasurybill with a face value of $10,000 will have a price of about $9,500, so that investors who buy the Treasury billhave the same rate of return as if they put their money into the bank and earned the interest. If the interestrate goes up, then the price investors will be willing to pay for the $10,000 Treasury bill necessarily goes down.

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What was the reason for these reactions? They might seem puzzling, consideringthe theory that an increase in the money supply works to lower the interest rate ratherthan to raise it. The first thing to realize is that the interest rate movements on Fridayafternoons were not directly caused by the changes in the money supply itself—whichhad taken place a week earlier—but rather by the effect of the new information onexpectations as to future monetary policy.

According to the theory of efficient markets, it is only the unanticipated compo-nent of the announced change in the money supply that matters. If the announcementreports an increase no larger than had been previously expected, then there should beno effect on prices in the bond market, foreign exchange market, or any other financialmarkets. Economists often refer to the importance of “news,” to signify that it is onlynew information that matters.

There are two possible different explanations for a rise in the nominal interest ratein response to a money announcement: a rise in the expected inflation rate or a rise inthe real interest rate. The rise in the nominal interest rate could be related to a rise inthe expected inflation rate, if investors concluded from the announcement of anincrease in the money supply that the Fed planned a faster rate of money growth in thefuture than had previously been expected. This is the case where investors do not putmuch credence in the money growth target that the Fed has announced for the yearand interpret deviations of the money supply from the previously expected path as evi-dence that the Fed has changed its target. Conversely, the rise in the nominal interestrate would be related to a rise in the real interest rate if investors interpret theannouncement as a sign that the Fed will tighten monetary policy in the near future.This is a reasonable thing to expect the Fed to do if the increase in the money stockoccurred for reasons beyond its control (e.g., banks can expand credit to a certaindegree, without there necessarily having been a change in Fed policy), and if it is seri-ously committed to keeping the money supply within its previously set target range. Inother words, this is the case where the Fed’s commitment to the preannounced target iscredible to the financial markets.

How is it possible to tell, at any particular time, which is the real cause of anincrease in the nominal interest rate? The foreign exchange market provides the answerto this question. If there is an expectation of looser monetary policy and higherexpected inflation, the exchange rate models predict that the dollar will fall on thenews. Conversely, if there is an expectation of tighter monetary policy and a higher realinterest rate, the dollar should rise on the news.

The evidence suggests that in the late 1970s, the Fed’s money growth targets werenot very credible. The dollar often fell in value immediately following announcementsof money supplies that were greater than had been expected. Investors worried aboutexcessive money growth and the inflationary consequences.

After October 1979, however, the Fed switched to a new set of operating proce-dures designed to set a firm course for the money supply, with the aim of fighting infla-tion. The pattern of reaction to the weekly money announcements switched as well. Inthe early 1980s there was a clear pattern in which both the interest rate and the dollarrose immediately in response to announced money figures that were greater thanexpected.This suggests (1) that investors during this period expected the Fed to correct

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27.5 ■ Two More Examples of the Importance of Expectations 601

deviations from the target, (2) that investors believe that monetary contraction raisesreal interest rates, and (3) that higher real interest rates make U.S. assets more attrac-tive and cause the dollar to appreciate, as in the overshooting model.29

The importance of the weekly money announcements diminished after 1982, whenthe Federal Reserve started paying less attention to the money supply because innova-tions in the banking sector and other shifts in the demand for money had taken muchof the meaning from M1 and the other traditional measures of monetary policy. TheFederal Reserve Board then stopped all pretense of setting M1 targets. As a result,interest rates and exchange rates no longer respond strongly to the money announce-ments. However, there are still macroeconomic variables that provoke major reactionswhen announced. After news suggesting strong economic growth, such as a decline inthe unemployment rate or an increase in retail sales or durable goods orders, the dollartends to appreciate. Investors figure, as in the monetary models, that higher domesticoutput raises the demand for domestic money.30 Similarly, when there is an announce-ment of a better trade balance than had been expected, the dollar tends to appreciate.31

Is Speculation Stabilizing?

It might seem that overshooting is an example of what is called destabilizing specula-tion—that investors, by freely buying and selling foreign exchange based on theirexpectations of changes in the exchange rate, make the exchange rate more variablethan it would otherwise be. This is not the case, however. The overshooting model justdeveloped illustrates the general principle that expectations are stabilizing rather thandestabilizing, as long as an increase in the level of the current exchange rate causesinvestors to reduce their expectations as to its future rate of change. (This is the case inregressive expectations, represented by Equation 27.14: S enters with a negative sign.)The reason is that if investors act on the basis of such expectations, they will buy thecurrency when its value is low and sell when its value is high. This will raise the cur-rency’s price when it would otherwise be low and lower the price when it would other-wise be high. This type of speculation works to moderate the fluctuations that wouldotherwise occur in the exchange rate.

Investors, or speculators, who buy low and sell high will also make a profit. This iswhy Milton Friedman argued that stabilizing speculators would prosper. Any specula-tors who were destabilizing would be buying high and selling low. They would losemoney and thus soon be driven out of business.

31The trade balance has no effect on the exchange rate in the model developed in this chapter (beyond theeffect of any of the other components of GDP ; C 1 I 1 G 1 X 2 M). This is a consequence of the assump-tion that when a country runs a trade deficit, the rest of the world is willing to lend it however much money itneeds to finance its deficits—regardless of how much debt it has already incurred in the past—so long as itpays the world rate of interest. The next chapter introduces a role for the debt, so that the trade balance againmatters for exchange rate determination.

30Gikas Hardouvelis, “Economic News, Exchange Rates and Interest Rates,” Journal of International Moneyand Finance, 7 (1988): 23–25.

29Charles Engel and Jeffrey Frankel, “Why Interest Rates React to Money Announcements: An Explanationfrom the Foreign Exchange Market,” Journal of Monetary Economics, 13 (1984): 31–39.

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It has sometimes been suggested that the government should try to discouragespeculation—for example, by enacting capital controls or a tax on foreign exchangetransactions, thereby returning the economy to a lower degree of international capitalmobility. James Tobin wrote that “we need to throw some sand in the well-greasedwheels” of international financial markets through a small tax on all foreign exchangetransactions.32 If investors act on the basis of the type of stabilizing expectations stud-ied here, Tobin’s proposal to discourage speculation would increase overshootingrather than reduce it, assuming the new barrier to international capital flows was effec-tive. If investors had to overcome a significant transaction cost to buy a foreign cur-rency, then the exchange rate would have to drift even further from its long-runequilibrium before the expectation of future appreciation was sufficiently great toinspire investors to buy it.

What, then, do proponents of such antispeculator taxes have in mind? They havein mind that speculators do not form expectations in a stabilizing manner, such as isgiven by Equation 27.14. Rather, they believe that speculators form their expectationsby simply extrapolating past trends. Such forecasting rules are called bandwagonexpectations: If investors actually act on the basis of them, they jump on the bandwagonwhenever the currency starts to move in one direction or the other. In such case, theycan create the sort of speculative bubbles described in Section 27.3. Investors buy whenthe currency is already high, thereby pushing it higher (until the bubble bursts); theysell the currency when it is already low, thereby pushing it lower. In such an environ-ment, speculation would indeed increase exchange rate volatility.

Which expectations, stabilizing or destabilizing, prevail in practice? Under normalcircumstances, when markets are functioning properly, economists believe that expec-tations are formed predominantly in a stabilizing manner. For example, during theperiod 1982 to 1984, because the dollar had risen above its PPP equilibrium, manyforecasters expected it to depreciate in the future.Any investors who acted on the basisof such expectations, far from being the cause of the appreciation of the dollar, wereselling dollars and thus dampening the price below what it would be otherwise.

There are times, however, when most market participants seem to lose sight ofeconomic fundamentals and to extrapolate trends instead. As noted earlier, someobservers have argued that July 1984 to February 1985 was such a period, with the finalappreciation of the dollar up to its peak attributable to a speculative bubble ratherthan to fundamentals. Figure 27.4 does make it appear this way: The 1985 spike in thedollar is a major movement in the exchange rate that does not correspond to a move-ment in the real interest rate differential. In this view, the dollar did more than over-shoot its long-run equilibrium; it overshot its short-run equilibrium as well.33 A similarovervaluation appeared in the years 2001 to 2002, particularly against the euro.

33Paul Krugman, “Is the Strong Dollar Sustainable?” The U.S. Dollar—Recent Developments, Outlook, andPolicy Options (Kansas City: Federal Reserve Bank of Kansas City, 1985), pp. 103–133.

32James Tobin, “A Proposal for International Monetary Reform,” Eastern Economic Journal, 4, nos. 3–4(1978): 153–159.

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27.6 ■ Summary 603

The view that the dollar was following a speculative bubble path by the end of1984 would be sympathetic to the switch at the U.S. Treasury from a noninterventionistpolicy of benign neglect of the dollar under Secretary Donald Regan from 1981 to1984, to a more activist policy under Secretary James Baker beginning in 1985. Theswitch was symbolized in September 1985 by the Plaza Accord, in which the financeministers of the G-5 countries agreed to try to bring the dollar down. The Plaza iswidely regarded as a case of successful management of the exchange rate by policymakers. Unfortunately, government officials are not always more skilled at identifyingwhen the exchange rate has departed from fundamentals than are private investors.

Keep in mind that the existence of a speculative bubble does not mean it is easyfor an investor to profit from it. The knowledge that the bubble must eventually burstdoes not mean investors can confidently expect to make money by moving intoanother currency (or “selling short”) because there is no telling how long the bubblewill continue, and the investor who does not go along with the trend will lose money aslong as it continues.

27.6 Summary

This chapter examined how monetary forces determine the exchange rate under a float-ing rate system. This required introducing exchange rate expectations, in addition tointerest rates, as a factor in determining investors’ decisions regarding what assets tohold. Modern models of exchange rate determination share the property of perfectinternational capital mobility. If there is also perfect substitutability between domesticand foreign bonds, then uncovered interest parity holds: The interest differential mustbe just large enough to offset investors’ expected depreciation of the domestic currency.

The chapter introduced a flexible-price version of the monetary model, in whichpurchasing power parity holds, which is relevant for long-run equilibrium. The result-ing equation shows how the exchange rate, as the relative price of two currencies, isdetermined by the supply and demand for two currencies. It is useful for seeing how (1)an exogenous increase in real income raises the demand for money and thus causes thecurrency to appreciate, (2) an increase in the current level of the money supply causesan immediate proportionate depreciation of the currency in equilibrium, and (3) anincrease in the expected future rate of growth of money and inflation causes an imme-diate fall in the equilibrium value of the currency.

These results pertain to long-run equilibrium. The rest of the chapter explainedthat the short-run equilibrium is characterized by overshooting. When the money sup-ply increases, the currency immediately depreciates more than proportionately; that is,it depreciates by more than it will in the long run. This is a consequence of goods pricesbeing sticky in the short run.The increase in the nominal money supply is an increase inthe real money supply. It reduces the interest rate, causing investors to shift theirdemand to foreign assets and causing the domestic currency to depreciate.This much issimilar to the effects of monetary expansion in the Mundell-Fleming model of Chap-ters 22 and 23. The new effect is that today’s depreciation generates the expectation

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among investors that the currency will in the future have to appreciate back towardlong-run equilibrium. This expectation of appreciation must be just sufficient to offsetthe interest differential, for investors to be willing to hold domestic assets. Thus when aloose monetary policy pushes the domestic real interest rate below the foreign realinterest rate, it will also push the real value of the currency below its usual level.

Modern models of exchange rate determination share another property: They aredesigned to fit the empirically observed high variability of floating exchange rates.These models explain such variability in three respects. First, because the exchangerate is seen to be determined in financial markets, it can be as volatile as the prices ofstocks, bonds, precious metals, and other assets. The expectation of a future loss in thevalue of the currency is enough to cause a large shift in demand and thus a large fall inthe equilibrium value of the currency today. Second, when goods prices adjust slowlybut asset markets adjust instantly, the exchange rate in the short run overshoots itslong-run equilibrium. Third, when a speculative bubble gets started, the exchange ratecan deviate even from the short-run equilibrium that is determined by the monetaryfundamentals.

CHAPTER PROBLEMS

1. If there is a downward shift in the demand for dollars because of increased use ofcredit cards, what is the effect on the exchange rate?

2. Assume in the monetary model with flexible prices that the public decides today themoney supply is expected to jump in the future. Draw the versions of the graphs of thefour variables that correspond to Figure 27.1.

3. a. If an investor were able to predict that a country’s currency will appreciate in the future because of a slower inflation rate in that country than in others, doesthis mean that the investor can necessarily earn a higher return by holding thatcurrency?

b. What if the investor were able to predict that a currency will appreciate in thefuture because it has already overshot (downward) its long-run equilibrium?

4. Are the following three statements true or false?i. If a country has a high interest rate, then its assets will be attractive to hold,

and so the value of the currency will be high.ii. If a country has a high interest rate, investors must expect that its currency

will lose value in the future.iii. If investors expect that a currency will lose value in the future, then they will

have a low demand for it and it will have a low value today.How do statements ii and iii together appear to contradict statement i? Can you recon-cile the three statements with each other? (Hint: It might help to distinguish why theinterest rate is high.)

5. The following is the balance-of-payments equilibrium condition from the Mundell-Fleming model, Equation 23.4, with exports depending on the exchange rate, S, and

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Suggestions for Further Reading 605

foreign income, Y*, and imports depending on Y. (All relationships here are assumedto be linear, and m and m* are the marginal propensities to import.)

xS 1 m*Y* 2 mY 1 1 k(i 2 i*) 5 0

a. Turn this equation into a model of exchange rate determination by solving for S.b. What policies determine i?c. Explain why the signs on Y, Y*, i, and i* here differ from those in Equation 27.8.

SUGGESTIONS FOR FURTHER READING

Dornbusch, Rudiger.“Expectations and Exchange Rate Dynamics,” Journal of PoliticalEconomy (December 1976): 1161–1176. The classic paper on the overshooting ofthe exchange rate in response to a change in the money supply.

Frankel, Jeffrey, and Andrew Rose. “Empirical Research on Nominal ExchangeRates.” In G. Grossman and K. Rogoff, eds., Handbook of International Economics(Amsterdam: Elsevier, 1995). A survey of studies, including the new “microstruc-ture” of the foreign exchange market.

Friedman, Milton. “The Case for Flexible Exchange Rates,” Essays in Positive Eco-nomics (Chicago: University of Chicago Press, 1953). The arguments for floating,twenty years ahead of their time.

Taylor, Mark. “The Economics of Exchange Rates,” Journal of Economic Literature,83, no. 1 (1995): 13–47. A survey of the literature on exchange rate determination,including the monetarist model, overshooting, target zones, and the news.

KA

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The Determination of Exchange Rates in International Asset ...PART VI The Determination of Exchange Rates in International Asset Markets Chapter 27 Expectations, Money, and the Determination